Cross-Domain Sequential Recommendation (CDSR) aims to en-hance recommendation quality by transferring knowledge across domains, offering effective solutions to data sparsity and cold-start issues. However, existing methods face three major limitations: (1) they overlook varying contexts in user interaction sequences, resulting in spurious correlations that obscure the true causal relationships driving user preferences; (2) the learning of domain- shared and domain-specific preferences is hindered by gradient conflicts between domains, leading to a seesaw effect where performance in one domain improves at the expense of the other; (3) most methods rely on the unrealistic assumption of substantial user overlap across domains. To address these issues, we propose CoDiS, a context-aware disentanglement framework grounded in a causal view to accurately disentangle domain-shared and domain-specific preferences. Specifically, Our approach includes a variational context adjustment method to reduce confounding effects of contexts, expert isolation and selection strategies to resolve gradient conflict, and a variational adversarial disentangling module for the thorough disentanglement of domain-shared and domain-specific representations. Extensive experiments on three real-world datasets demonstrate that CoDiS consistently outperforms state-of-the-art CDSR baselines with statistical significance. Code is available at:https://anonymous.4open.science/r/CoDiS-6FA0.